We develop a parallel algorithm that calculates the exact partition function of a lattice polymer,
by enumerating the number of conformations for each energy level. An efficient parallelization
of the calculation is achieved by classifying the conformations according to the shape of the box
spanned by a conformation, and enumerating only those in a given box at a time. The calculation
time for each box is reduced by preventing the conformations related by symmetry from being
generated more than once. The algorithm is applied to study the collapse transition of a lattice
homopolymer on a square lattice, by calculating the specific heat for chain lengths up to 36.